diff --git a/.gitignore b/.gitignore
index 73e203a64..86bab2717 100644
--- a/.gitignore
+++ b/.gitignore
@@ -30,3 +30,4 @@ node_modules/
__pycache__/
*.pyc
spec/**/generated
+tmp/
\ No newline at end of file
diff --git a/spec/API_specification/array_api/elementwise_functions.py b/spec/API_specification/array_api/elementwise_functions.py
index 7acefaf52..43e5132d7 100644
--- a/spec/API_specification/array_api/elementwise_functions.py
+++ b/spec/API_specification/array_api/elementwise_functions.py
@@ -427,12 +427,20 @@ def cos(x: array, /) -> array:
"""
def cosh(x: array, /) -> array:
- """
- Calculates an implementation-dependent approximation to the hyperbolic cosine, having domain ``[-infinity, +infinity]`` and codomain ``[-infinity, +infinity]``, for each element ``x_i`` in the input array ``x``.
+ r"""
+ Calculates an implementation-dependent approximation to the hyperbolic cosine for each element ``x_i`` in the input array ``x``.
+
+ The mathematical definition of the hyperbolic cosine is
+
+ .. math::
+ \operatorname{cosh}(x) = \frac{e^x + e^{-x}}{2}
**Special cases**
- For floating-point operands,
+ .. note::
+ For all operands, ``cosh(x)`` must equal ``cosh(-x)``.
+
+ For real-valued floating-point operands,
- If ``x_i`` is ``NaN``, the result is ``NaN``.
- If ``x_i`` is ``+0``, the result is ``1``.
@@ -440,15 +448,38 @@ def cosh(x: array, /) -> array:
- If ``x_i`` is ``+infinity``, the result is ``+infinity``.
- If ``x_i`` is ``-infinity``, the result is ``+infinity``.
+ For complex floating-point operands, let ``a = real(x_i)``, ``b = imag(x_i)``, and
+
+ .. note::
+ For complex floating-point operands, ``cosh(conj(x))`` must equal ``conj(cosh(x))``.
+
+ - If ``a`` is ``+0`` and ``b`` is ``+0``, the result is ``1 + 0j``.
+ - If ``a`` is ``+0`` and ``b`` is ``+infinity``, the result is ``NaN + 0j`` (sign of the imaginary component is unspecified).
+ - If ``a`` is ``+0`` and ``b`` is ``NaN``, the result is ``NaN + 0j`` (sign of the imaginary component is unspecified).
+ - If ``a`` is a nonzero finite number and ``b`` is ``+infinity``, the result is ``NaN + NaN j``.
+ - If ``a`` is a nonzero finite number and ``b`` is ``NaN``, the result is ``NaN + NaN j``.
+ - If ``a`` is ``+infinity`` and ``b`` is ``+0``, the result is ``+infinity + 0j``.
+ - If ``a`` is ``+infinity`` and ``b`` is a nonzero finite number, the result is ``+infinity * cis(b)``.
+ - If ``a`` is ``+infinity`` and ``b`` is ``+infinity``, the result is ``+infinity + NaN j`` (sign of the real component is unspecified).
+ - If ``a`` is ``+infinity`` and ``b`` is ``NaN``, the result is ``+infinity + NaN j``.
+ - If ``a`` is ``NaN`` and ``b`` is either ``+0`` or ``-0``, the result is ``NaN + 0j`` (sign of the imaginary component is unspecified).
+ - If ``a`` is ``NaN`` and ``b`` is a nonzero finite number, the result is ``NaN + NaN j``.
+ - If ``a`` is ``NaN`` and ``b`` is ``NaN``, the result is ``NaN + NaN j``.
+
+ where ``cis(v)`` is ``cos(v) + sin(v)*1j``.
+
+ .. note::
+ The hyperbolic cosine is an entire function in the complex plane and has no branch cuts. The function is periodic, with period :math:`2\pi j`, with respect to the imaginary component.
+
Parameters
----------
x: array
- input array whose elements each represent a hyperbolic angle. Should have a real-valued floating-point data type.
+ input array whose elements each represent a hyperbolic angle. Should have a floating-point data type.
Returns
-------
out: array
- an array containing the hyperbolic cosine of each element in ``x``. The returned array must have a real-valued floating-point data type determined by :ref:`type-promotion`.
+ an array containing the hyperbolic cosine of each element in ``x``. The returned array must have a floating-point data type determined by :ref:`type-promotion`.
"""
def divide(x1: array, x2: array, /) -> array:
pFad - Phonifier reborn
Pfad - The Proxy pFad of © 2024 Garber Painting. All rights reserved.
Note: This service is not intended for secure transactions such as banking, social media, email, or purchasing. Use at your own risk. We assume no liability whatsoever for broken pages.
Alternative Proxies:
Alternative Proxy
pFad Proxy
pFad v3 Proxy
pFad v4 Proxy